The present invention relates generally to a relief type diffraction optical element of sawtooth shape in section, an optical system comprising a relief type diffraction optical element and a method of designing the optical system, and more particularly to a relief type diffraction optical element having a lens action.
A lens (diffractive lens) bending light by diffraction has a unique yet useful feature different from the feature of a refractive lens. For instance, it is possible to achieve an achromatic optical system by making use of a diffractive lens having dispersions (inverse and anomalous dispersions) different from those of a refractive lens, and reduce the size and weight of an optical system by making use of the feature of the diffractive lens that has substantially no thickness. Such a diffractive lens can be fabricated in the form of a relief type diffractive element by use of recent micromachining technologies. Recently, applications with an actually mounted diffractive lens have been put to practical use. Thus, diffractive lenses have already been at the commercial stage.
However, a diffractive optical element represented by a diffractive lens has a unique property called diffraction efficiency that is not found a refractive element. In some cases, this property is a deterrent to the application of a diffractive lens to a phototaking optical element. One example of that property is the angle-of-incidence dependence of diffraction efficiency. Even though a diffractive optical element is constructed in such a manner that sufficient diffraction efficiency is obtainable at a specific angle of incidence, the diffraction efficiency often drops with a change in the angle of incidence--a phenomenon called the angle-of-incidence dependence of diffraction efficiency. In principle, this problem is inherent to every diffractive optical element. Given an actual diffractive optical element, this problem arises necessarily to one degree or another.
A lowering of diffraction efficiency with respect to major orders of light is tantamount to an increase in other orders of light (unnecessary light). Such unnecessary light takes the form of ghosts or flares, causing a deterioration in the performance of an optical system. Even when a diffractive lens is used in a photodetection optical system such as a pickup lens, it is therefore desired to achieve at least 60% diffraction efficiency. Especially when the diffractive lens is used in an image formation optical system to form images, at least 80% diffraction efficiency is needed so as to keep a minimum of image quality. To achieve high-definition image quality, at least 90% diffraction efficiency, or at least 95% diffraction efficiency in some cases, is needed.
In some cases, grooves in a relief type diffractive optical element, for instance, are made flat by use of a transparent optical material. The diffractive optical element of such construction is characterized by being resistant to extraneous contamination because the fine structure of a relief pattern is protected, and so enables such optical design as to expose a relief pattern surface substantially to the outside. This technique is very effective to put a diffractive optical element to practical use. However, this construction may possibly make the angle-of-incidence dependence of diffraction efficiency worse than that of an ordinary relief grating. Therefore, when this construction is applied to an actual optical system, it is very important to pay quantitative attention to the angle-of-incidence dependence of diffraction efficiency.
To apply a diffractive optical element to an optical system for practical purposes, it is then inevitable to pay quantitative attention to the angle-of-incidence dependence of diffraction efficiency. In such an ordinary method of designing a diffractive lens as represented by an ultrahigh index method (Sweatt Model) wherein a diffractive optical element is substituted by a virtual refractive lens, however, whether the diffractive optical element is a relief grating or a volume hologram is not designated at the design stage. The angle-of-incidence dependence of diffraction efficiency varies for each embodiment of the diffractive optical element. In other words, such a design method cannot achieve design with the angle-of-incidence dependence of diffraction efficiency in mind. Even though an optical system comprising a diffractive optical element is constructed according to such design, the optical properties as designed would often be unexpectable.
As one means for providing quantitative analysis of the angle-of-incidence dependence of diffraction efficiency in a relief type diffractive optical element, electric field analysis based on Maxwell's equations is generally available. Electric field analysis based on Maxwell's equations may make it possible to have a quantitative understanding of the angle-of-incidence dependence of diffraction efficiency. When this method is used, however, it is not easy to obtain the results of calculation, because a solution of a differential equation should be found for each specific state (the wavelength of light used, grating pitch, groove depth, refractive index, and so on). To obtain a solution of the differential equation, approximately P.times.P matrix calculations are needed at a pitch P standardized with wavelength. At a pitch level (usually 20 or more pitches standardized with wavelength) often used for a diffractive lens in an image formation optical system, it is very difficult to obtain the results of calculation. Thus, it is impractical to perform such analysis parallel with lens design.
As another means for estimating the diffraction efficiency of a relief type diffractive element, a method of applying a thin diffraction grating model (thin model) to Scalar diffraction formula is available. This method has a feature of making it possible to easily obtain the results of calculation, because the diffraction efficiency of the relief type diffractive element is described by a formulated (so-called closed form of) expression. However, the method based on such a thin model is little applied to the estimation of the angle-of-incidence dependence of diffraction efficiency that is one specific object of the invention, because no care is generally taken of the influence of oblique incidence. In a model obtained by extension of the thin model (E. K. Popov et al., Opt. Commun. 80, (1991) 307), care is taken of the oblique incidence feature of the relief grating. This model, too, is not sufficient in terms of quantitative accuracy with which diffraction efficiency is quantitatively estimated as contemplated in the invention. Especially when grooves in the relief type diffractive optical element are made flat with a transparent optical material, the results obtained in this method are in no quantitative coincidence with the results of stringent calculation based on electric field analysis at all.
As explained above, any method of making quantitative estimation of the diffraction efficiency of a relief type diffractive optical element including its angle-of-incidence dependence in an easy manner has not been established in the prior art. For this reason, little care is taken of the angle-of-incidence dependence of diffraction efficiency of an optical system at the design stage; there is a large significant difference between the optical performance and the design performance of an actually constructed optical system.